A Manhattan woman carried a switchblade knife through a La Guardia Airport checkpoint yesterday — after a TSA agent spotted it in her purse as she passed through an X-ray machine, police sources told The Post.

The incredible screw-up by the Transportation Security Administration happened at 10:05 a.m. as Kelly Polonus, 24, headed to her Charlotte, NC-bound flight, the sources said.

When TSA Agent Michael Sanchez saw the weapon, he told a colleague to search her bags.

But that screener, Richard Camacho, mistakenly thought he’d been ordered to look for liquids. He did that search and let her through, the sources said.

Sanchez finally realized the mistake five minutes later — and he called in Port Authority cops.

Cops found Polonus at a gate, and seized the knife.

“My father gave it to me when I moved to New York,” said the woman, a Georgia native who now lives on the Lower East Side.